EE 446/646 Photovoltaic Devices II

Y. Baghzouz

The p-n junction diode

• Before discussing the case when a p-n junction is exposed to sunlight, it is worth reviewing the p-n junction diode since it has some common electrical characteristics.

• A diode is an electronic component that consists of a p-n junction, just like a solar cell, except that it has a much smaller surface and the semiconductor material is not exposed as both sides are entirely covered with electrical contact material.

• With no external voltage, a diode is basically a p-n junction that is under equilibrium between diffusion and drift currents, as described earlier.

Diode Under Forward Bias

• When a voltage is applied across the

terminals of a diode with the positive

side connected to the p-type material

and the negative side connected to the

n-type material, the diode is said to be

in the forward bias state.

• In forward bias, the applied electric field

by the voltage source is in opposite

direction of that of the built-in electric

field in the depletion region.

• The net electric field is weakened, thus

reducing the barrier to the diffusion of

carriers from one side of the junction to

the other. This results in an increase in

the diffusion current.

Diode Under Forward Bias

• The majority carriers are supplied from

the external circuit, hence resulting in a

net current flows under forward bias.

• In a semiconductor, the minority

carriers recombine and thus more

carriers can diffuse across the junction.

• Consequently, the diffusion current

which flows in forward bias is a

recombination current. The higher the

rate of recombination events, the

greater the current flow.

Diode Under Reverse Bias

• In reverse bias, a voltage is applied across the device is such that the electric field at the junction increases.

• The higher electric field in the depletion region decreases the probability that carriers can diffuse from one side of the junction to the other, hence the diffusion current decreases.

• As in forward bias, the drift current is limited by the number of minority carriers on either side of the p-n junction, and is relatively unchanged by the increased electric field.

p-n junction diode - recap

– When a forward voltage Vd is applied across the diode terminals, current would flow easily through the diode from the p-side to the n-side. The forward voltage across the diode is only a few tenths of a volt.

– If we try to send current in the reverse direction, only a very small (nA - pA ) reverse saturation current I0 will flow (result of thermally generated carriers with the holes being swept into the p-side and the electrons into the n-side). I0 is often referred to as the “dark saturation current”.

Diode voltage-current characteristic

• The voltage– current characteristic curve for the p –n junction

diode is described by the following Shockley diode equation:

• where q is the electron charge (1.602 × 10 −19 C), k is

Boltzmann’s constant (1.381 × 10−23 J/K), and T is the junction

temperature (K), and Io is the dark saturation current.

@ 25oC

Ideality Factor

• In general,

• where A is the ideality factor.

– A = 1 if the transport process is purely diffusion,

– A = 2 if the transport process is primarily recombination in the

depletion region.

p-n junction cell exposed to sunlight • When placed in the dark, a photovoltaic cell behaves like a p-n

junction diode. When it is exposed to sunlight.

– Photons with sufficient energy are absorbed by the semiconductor

and form hole-electron pairs.

– If these mobile charge carriers reach the vicinity of the junction

before they recombine, the electric field in the depletion region will

push the holes into the p-side and push the electrons into the n-side.

Hence, the p-side accumulates more holes and the n-side

accumulates more electrons.

p-n junction cell exposed to sunlight • This separation of charge creates an electric field at the junction

which is in opposition to that already existing at the junction, hence

a weaker net electric field which increases the diffusion current.

• If the light-generated carriers are prevented from leaving the solar

cell, the forward bias of the junction increases to a point where the

light-generated current is exactly balanced by the forward bias

diffusion current, and the net current is zero. The resulting voltage

at the cell terminals under this condition is called the open-circuit

voltage.

p-n junction cell exposed to sunlight • when the cell terminals are connected to an external circuit, the light-

generated electrons are provided an external path, while the holes remain stuck in the p-type semiconductor since they cannot flow through wire.

• Herein, the electrons will flow out of the n-side through the connecting wire to the load, and then recombine with holes that are waiting on the p-side.

• In this case, the forward bias of the junction decreases to a point where the light-generated current is equal to the current supplied to the load (which is equal to electron drift minus electron diffusion). The result is a decrease in diffusion current due to an increase in the net electric field across the junction.

Generic PV cell

• When a p –n junction is exposed to sunlight,

– As photons are absorbed, hole-electron pairs may be formed.

– If these mobile charge carriers reach the vicinity of the

junction, the electric field in the depletion region will push the

holes into the p-side and push the electrons into the n-side.

– The p-side accumulates holes and the n-side accumulates

electrons, This creates a stronger electric field, and hence

stronger voltage.

External current flow

– If electrical contacts are attached to the top and bottom of the cell, electrons will flow out of the n-side into the connecting wire, through the load and back to the p-side (a wire cannot conduct holes).

– When they reach the p-side, they recombine with holes completing the circuit.

– By convention, positive current flows in the direction opposite to electron flow.

Simple Equivalent Circuit

• A simple equivalent circuit model for a photovoltaic cell consists of a real diode in parallel with an ideal current source.

• The ideal current source delivers current in proportion to the solar flux to which it is exposed.

Short-circuit current and open-circuit voltage

• The short-circuit current ISC is defined as the current that flows when the terminals are shorted together. This is equal to the magnitude of the ideal current source.

• The open-circuit voltage VOC is defined as the voltage across the terminals when the leads are left open.

Current-voltage relation

• Relation between the short-circuit, diode, and load currents:

• Substituting the diode current equation:

• At 25oC,

I-V Curve

• The open-circuit voltage can be found by setting the load current to zero:

• At 25oC,

Example

• Consider a 100-cm2 photovoltaic cell with reverse saturation current Io = 10−12 A/cm2 . In full sun, it produces a short-circuit current of 40 mA/cm2 at 25o C. Find the open-circuit voltage at full sun and again for 50% sunlight. Plot the results.

A more accurate equivalent circuit

• Addition of parallel leakage resistance RP to account for manufacturing defects

• The ideal current source ISC in this case delivers current to the diode, the parallel resistance, and the load:

• For a cell to have losses of less than 1% due to its parallel resistance, RP should be greater than 100VOC/ISC.

A more accurate equivalent circuit

• Addition of series resistance RS to account for the resistance to the movement of current through the p-n materials; the contact resistance between metal and silicon; the resistance of the top and rear metal contacts.

• The diode voltage and load voltage are related by

• For a cell to have losses of less than 1% due to its series resistance, RS should be greater than 0.01VOC/ISC.

Final accurate equivalent circuit

• Addition of both series resistance RS and parallel resistance RP.

• The current –voltage equation becomes (non explicit)

• At 25oC,

Useful current-voltage relationships

• Short circuit current in terms of load current, diode current, and parallel resistor current

• Load current in terms of diode current, short-circuit current and diode voltage

• Relation between load voltage and diode voltage

Problems E = hv = hc/λ

P = VI Pout = VI

η = Pout/Pin

Problems

• P = VI

• η = Pout/Pin

• Rp = V/ΔI = 0.4/0.2 = 2Ω

Problems

• Rs = ΔV/I = 0.04/1 = 0.04 Ω

• P = VI

Consider the cell equivalent circuit below. The following Parameters are known: Isc, Io, Cell temp, Rp, Rs and Vd. 1) Compute the power supplied by the cell.